integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees. Integer triangles with a 120° angle Integer triangles with a 120° angle can be generated by with coprime integers m, n with 0 < n < m (the angle of 120° is opposite to the side of length a). From here, all primitive solutions can be obtained by dividing a, b, and c by their greatest common divisor. The smallest solution, for m = 2 and n = 1, is the triangle with sides (3,5,7). See also. More precisely, If , then , otherwise . Since the biggest side a can only be generated with a single pair, each primitive triple can be generated in precisely two ways: once directly with gcd = 1, and once indirectly with gcd = 3. Therefore, in order to generate all primitive triples uniquely, one can just add additional condition. Integer triangles with one angle equal to an arbitrary rational number times another angle For positive coprime integers h and k, the triangle with the following sides has angles , , and and hence two angles in the ratio h : k, and its sides are integers: where and p and q are any coprime integers such that . Integer triangles with one angle equal to twice another With angle A opposite side and angle B opposite side , some triangles with B = 2A are generated by with integers m, n such that 0 < n < m < 2n. All triangles with B = 2A (whether integer or not) satisfy Integer triangles with one angle equal to 3/2 times another The equivalence class of similar triangles with are generated by with integers such that , where is the golden ratio . All triangles with (whether with integer sides or not) satisfy Integer triangles with one angle three times another We can generate the full equivalence class of similar triangles that satisfy B = 3A by using the formulas where and are integers such that . All triangles with B = 3A (whether with integer sides or not) satisfy Integer triangles with three rational angles The only integer triangle with three rational angles (rational numbers of degrees, or equivalently rational fractions of a full turn) is the equilateral triangle. This is because integer sides imply three rational cosines by the law of cosines, and